System and method for multi-material correction of image data

ABSTRACT

A method is provided. The method includes acquiring projection data of an object from a plurality of pixels, reconstructing the acquired projection data from the plurality of pixels into a reconstructed image, performing material characterization and decomposition of an image volume of the reconstructed image to reduce a number of materials analyzed in the image volume to two basis materials. The method also includes generating a re-mapped image volume for at least one basis material of the two basis materials, and performing forward projection on at least the re-mapped image volume for the at least one basis material to produce a material-based projection. The method further includes generating multi-material corrected projections based on the material-based projection and a total projection attenuated by the object, which represents both of the two basis materials, wherein the multi-material corrected projections include linearized projections.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of patent application Ser. No.13/677,010, entitled “System and Method for Multi-Material Correction ofImage Data,” filed Nov. 14, 2012, which is herein incorporated byreference in its entirety for all purposes.

BACKGROUND

Non-invasive imaging technologies allow images of the internalstructures or features of a patient to be obtained without performing aninvasive procedure on the patient. In particular, such non-invasiveimaging technologies rely on various physical principles, such as thedifferential transmission of X-rays through the target volume or thereflection of acoustic waves, to acquire data and to construct images orotherwise represent the observed internal features of the patient.

For example, in computed tomography (CT) and other X-ray based imagingtechnologies, X-ray radiation spans a subject of interest, such as ahuman patient, and a portion of the radiation impacts a detector wherethe image data is collected. In digital X-ray systems a photodetectorproduces signals representative of the amount or intensity of radiationimpacting discrete pixel regions of a detector surface. The signals maythen be processed to generate an image that may be displayed for review.In CT systems a detector array, including a series of detector elements,produces similar signals through various positions as a gantry isdisplaced around a patient.

In the images produced by such systems, it may be possible to identifyand examine the internal structures and organs within a patient's body.However, the produced images may also include artifacts that adverselyaffect the quality of the images due to a variety of factors. Forexample, these factors may include beam hardening for non-watermaterials, heel-effect related spectral variation in wide cone CTsystems, bone induced spectral (BIS) due to detection variation ofdifferent detector pixels coupled to spectral changes attenuated by boneor other non-water materials, and other factors. Present techniques tocorrect for these artifacts are empirically based and inaccurate.

BRIEF DESCRIPTION

In accordance with a first embodiment, a method is provided. The methodincludes acquiring projection data of an object from a plurality ofpixels, reconstructing the acquired projection data from the pluralityof pixels into a reconstructed image, performing materialcharacterization and decomposition of an image volume of thereconstructed image to reduce a number of materials analyzed in theimage volume to two basis materials. The method also includes generatinga re-mapped image volume for at least one basis material of the twobasis materials, and performing forward projection on at least there-mapped image volume for the at least one basis material to produce amaterial-based projection. The method further includes generatingmulti-material corrected projections based on the material-basedprojection and a total projection attenuated by the object, whichrepresents both of the two basis materials, wherein the multi-materialcorrected projections include linearized projections.

In accordance with a second embodiment, one or more non-transitorycomputer readable media are provided. The computer-readable media encodeone or more processor-executable routines. The one or more routines,when executed by a processor, cause acts to be performed including:acquiring projection data of an object from a plurality of pixels,reconstructing the acquired projection data from the plurality of pixelsinto a reconstructed image, and performing material characterization anddecomposition of the image volume of the reconstructed image to reduce anumber of materials analyzed in the image volume to two basis materials.The acts to be performed also include generating a re-mapped imagevolume for at least one basis material of the two basis materials, andperforming forward projection on at least the re-mapped image volume forthe at least one basis material to produce a material-based projection.The acts to be performed further include generating multi-materialcorrected projections based on the material-based projection and aspectrally corrected total raw projection attenuated by the object,which represents both of the two basis materials, wherein themulti-material corrected projections include linearized projections.

In accordance with a third embodiment, a system is provided. The systemincludes a memory structure encoding one or more processor-executableroutines. The routines, when executed, cause acts to be performedincluding: acquiring projection data of an object from a plurality ofpixels, reconstructing the acquired projection data from the pluralityof pixels into a reconstructed image, performing materialcharacterization and decomposition of an image volume of thereconstructed image to reduce a number of materials analyzed in theimage volume to two basis materials, iodine and water. The acts to beperformed also include generating a re-mapped image volume for at leastiodine, and performing forward projection on at least the re-mappedimage volume for iodine to produce an iodine-based projection. The actsto be performed further include generating multi-material correctedprojections based the iodine-based projection and a spectrally correctedtotal raw projection attenuated by the object, which represents bothwater and iodine, wherein the multi-material corrected projectionsinclude linearized projections. The system also includes a processingcomponent configured to access and execute the one or more routinesencoded by the memory structure.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the present subjectmatter will become better understood when the following detaileddescription is read with reference to the accompanying drawings in whichlike characters represent like parts throughout the drawings, wherein:

FIG. 1 is a schematic illustration of an embodiment of a computedtomography (CT) system configured to acquire CT images of a patient andto process the images in accordance with aspects of the presentdisclosure;

FIG. 2 is a process flow diagram of an embodiment of a method forperforming multi-material correction on projection data;

FIG. 3 is a detailed process flow diagram of an embodiment of a methodfor performing multi-material correction on projection data thatutilizes water and iodine as basis materials; and

FIG. 4 is a continuation of the method of FIG. 3.

DETAILED DESCRIPTION

While the following discussion is generally provided in the context ofmedical imaging, it should be appreciated that the present techniquesare not limited to such medical contexts. Indeed, the provision ofexamples and explanations in such a medical context is only tofacilitate explanation by providing instances of real-worldimplementations and applications. However, the present approaches mayalso be utilized in other contexts, such as the non-destructiveinspection of manufactured parts or goods (i.e., quality control orquality review applications), and/or the non-invasive inspection ofpackages, boxes, luggage, and so forth (i.e., security or screeningapplications).

Tissue characterization or classification may be desirable in variousclinical contexts to assess the tissue being characterized forpathological conditions and/or to assess the tissue for the presence ofvarious elements, chemicals or molecules of interest. However, tissuecharacterization in imaging studies, such as using computed tomography(CT), may be problematic due to the presence of artifacts present withinthe reconstructed images. These artifacts may be present due to avariety of sources. For instance, due to the nature of a polychromaticX-ray beam produced by the Bremsstrahlung process, the beam attenuatedby different materials of an imaged subject will result in differentexit beam spectra. The effect of the polychromatic nature of the inputX-ray spectra and the energy-dependent nature of material attenuation bydifferent materials induces “beam hardening” artifacts in thereconstructed image. In addition, the mean value of a given material isnot constant. For example, presently the CT value of a non-watermaterial is a function of the incident beam, location of the materials,type of reconstruction due to weighting, and adjacent materials around aregion of interest (ROI). However, from a physics point of view, thepresence of the beam hardening artifact is due to a single reason, themeasured projections of a given type of material is not linearlyproportional to the length of the material at different view angles.

Further factors also result in artifacts in the reconstructed images.For example, the “heel-effect” causes incident beam spectrum variationinside a wide cone angle, especially a beam with a few degrees take-offangle from the anode. The heel-effect results in different mean valuesof non-water materials across the cone angle. Another factor is due tothe detection system in any clinical CT system not being perfect. Forexample, each detector pixel might have a slightly different response togiven incident spectrum, resulting in differential errors in detectionwhen the incident beam is not purely water-attenuated, causing abone-induced spectral (BIS) artifact. Typically, iterative bone option(IBO) and BIS correction techniques used to correct these artifacts areempirically based and/or subject to error.

As discussed herein, in various implementations, a multi-materialcorrection (MMC) approach is employed to compensate for artifacts withinthe reconstructed images. In particular, the MMC approach (e.g.,algorithm) is designed to deal with the different sources ofbeam-hardening related issues described above with a singlelinearization correction to minimize artifacts that are not corrected bywater-based spectral calibration and correction. The MMC approach isbased on the underlying physics model, as opposed to being empiricallybased. In addition, the MMC approach linearizes the detection of all thematerials present to eliminate beam hardening from its root cause,regardless of the material type, thus, resulting in more accurate andconsistent CT values of bone, soft tissue, and contrast agent for betterclinical diagnosis. Thus, the MMC approach minimizes the beam-hardeningartifacts in the images that originate from bone, contrast agent, andmetal implants. Additional direct clinical benefits due to the MMCapproach include improved image quality, better differentiation betweencysts and metastases, better delineation of bone-brain interface andaccurate contrast measurement in CT perfusion. Further, the value of thecontrast agent or bone can be corrected to be only kVp dependent, ormore precisely, effective keV dependent, which is close to offering amonochromatic beam. Yet further, in contrast to the current techniquesused with clinical CT systems, the MMC approach is not dependent onpatient size or the location of the region-of-interest (ROI). Thus, theMMC approach may provide a technique for providing accurate CT valuesfor contrast agent and bone.

With the foregoing discussion in mind, FIG. 1 illustrates an embodimentof an imaging system 10 for acquiring and processing image data inaccordance with aspects of the present disclosure. In the illustratedembodiment, system 10 is a computed tomography (CT) system designed toacquire X-ray projection data, to reconstruct the projection data into atomographic image, and to process the image data for display andanalysis. The CT imaging system 10 includes an X-ray source 12. Asdiscussed in detail herein, the source 12 may include one or more X-raysources, such as an X-ray tube or solid state emission structures. TheX-ray source 12, in accordance with present embodiments, is configuredto emit an X-ray beam 20 at one or more energies. Although the followingtechniques discussed below utilize the emission of the beam at a singleemission spectrum, the same techniques may be applied for the emissionof the beam at two or more energies, although single-energy embodimentsare discussed herein to simplify explanation. For example, the X-raysource 12 may be configured to switch between relatively low energypolychromatic emission spectra (e.g., at about 80 kVp) and relativelyhigh energy polychromatic emission spectra (e.g., at about 140 kVp).Also, the X-ray source 12 may emit at polychromatic spectra localizedaround energy levels (i.e., kVp ranges) other than those listed herein(e.g., 100 kVP, 120 kVP, etc.). Indeed, selection of the respectiveenergy levels for emission may be based, at least in part, on theanatomy being imaged.

In certain implementations, the source 12 may be positioned proximate toa collimator 22 used to define the size and shape of the one or moreX-ray beams 20 that pass into a region in which a subject 24 (e.g., apatient) or object of interest is positioned. The subject 24 attenuatesat least a portion of the X-rays. Resulting attenuated X-rays 26 impacta detector array 28 formed by a plurality of detector elements. Eachdetector element produces an electrical signal that represents theintensity of the X-ray beam incident at the position of the detectorelement when the beam strikes the detector 28. Electrical signals areacquired and processed to generate one or more scan datasets.

A system controller 30 commands operation of the imaging system 10 toexecute examination and/or calibration protocols and to process theacquired data. With respect to the X-ray source 12, the systemcontroller 30 furnishes power, focal spot location, control signals andso forth, for the X-ray examination sequences. The detector 28 iscoupled to the system controller 30, which commands acquisition of thesignals generated by the detector 28. In addition, the system controller30, via a motor controller 36, may control operation of a linearpositioning subsystem 32 and/or a rotational subsystem 34 used to movecomponents of the imaging system 10 and/or the subject 24. The systemcontroller 30 may include signal processing circuitry and associatedmemory circuitry. In such embodiments, the memory circuitry may storeprograms, routines, and/or encoded algorithms executed by the systemcontroller 30 to operate the imaging system 10, including the X-raysource 12, and to process the data acquired by the detector 28 inaccordance with the steps and processes discussed herein. In oneembodiment, the system controller 30 may be implemented as all or partof a processor-based system such as a general purpose orapplication-specific computer system.

The source 12 may be controlled by an X-ray controller 38 containedwithin the system controller 30. The X-ray controller 38 may beconfigured to provide power and timing signals to the source 12. Inaddition, in some embodiments the X-ray controller 38 may be configuredto selectively activate the source 12 such that tubes or emitters atdifferent locations within the system 10 may be operated in synchronywith one another or independent of one another. The X-ray controller 38is configured to control the source 12 to emit X-rays at a singlepolychromatic energy spectrum in an image acquisition sequence toacquire a single energy dataset. In certain embodiments, the X-raycontroller 38 may be configured to provide fast-kVp switching of theX-ray source 12 so as to rapidly switch the source 12 to emit X-rays atthe respective different polychromatic energy spectra in successionduring an image acquisition session. For example, in a dual-energyimaging context, the X-ray controller 38 may operate the X-ray source 12so that the X-ray source 12 alternately emits X-rays at the twopolychromatic energy spectra of interest, such that adjacent projectionsare acquired at different energies (i.e., a first projection is acquiredat high energy, the second projection is acquired at low energy, thethird projection is acquired at high energy, and so forth). In one suchimplementation, the fast-kVp switching operation performed by the X-raycontroller 38 yields temporally registered projection data. In someembodiments, other modes of data acquisition and processing may beutilized. For example, a low pitch helical mode, rotate-rotate axialmode, N×M mode (e.g., N low-kVp views and M high-kVP views) may beutilized to acquire dual-energy datasets.

As noted above, the X-ray source 12 may be configured to emit X-rays atone or more energy spectra. Though such emissions may be generallydescribed or discussed as being at a particular energy (e.g., 80 kVp,140 kVp, and so forth), the respective X-ray emissions at a given energyare actually along a continuum or spectrum and may, therefore,constitute a polychromatic emission centered at, or having a peakstrength at, the target energy.

The system controller 30 may include a data acquisition system (DAS) 40.The DAS 40 receives data collected by readout electronics of thedetector 28, such as sampled analog signals from the detector 28. TheDAS 40 may then convert the data to digital signals for subsequentprocessing by a processor-based system, such as a computer 42. In otherembodiments, the detector 28 may convert the sampled analog signals todigital signals prior to transmission to the data acquisition system 40.The computer 42 may include or communicate with one or morenon-transitory memory devices 46 that can store data processed by thecomputer 42, data to be processed by the computer 42, or instructions tobe executed by a processor 44 of the computer 42. For example, aprocessor of the computer 42 may execute one or more sets ofinstructions stored on the memory 46, which may be a memory of thecomputer 42, a memory of the processor, firmware, or a similarinstantiation. In accordance with present embodiments, the memory 46stores sets of instructions that, when executed by the processor,perform image processing methods as discussed herein (e.g., performanceof MMC).

The computer 42 may also be adapted to control features enabled by thesystem controller 30 (i.e., scanning operations and data acquisition),such as in response to commands and scanning parameters provided by anoperator via an operator workstation 48. The system 10 may also includea display 50 coupled to the operator workstation 48 that allows theoperator to view relevant system data, imaging parameters, raw imagingdata, reconstructed data, contrast agent density maps produced inaccordance with the present disclosure, and so forth. Additionally, thesystem 10 may include a printer 52 coupled to the operator workstation48 and configured to print any desired measurement results. The display50 and the printer 52 may also be connected to the computer 42 directlyor via the operator workstation 48. Further, the operator workstation 48may include or be coupled to a picture archiving and communicationssystem (PACS) 54. PACS 54 may be coupled to a remote system 56,radiology department information system (RIS), hospital informationsystem (HIS) or to an internal or external network, so that others atdifferent locations can gain access to the image data.

Keeping in mind the operation of the system 10 and, specifically, theX-ray source 12 discussed above with respect to FIG. 1, FIG. 2illustrates a process flow diagram of an embodiment of a method 58 forperforming MMC on projection data (e.g., datasets). Any suitableapplication-specific or general-purpose computer having a memory andprocessor may perform some or all of the steps of the method 58. By wayof example, as noted above with respect to FIG. 1, the computer 42 andassociated memory 46 may be configured to perform the method 58. Forexample, the memory 46, which may be any tangible, non-transitory,machine-readable medium (e.g., an optical disc, solid state device,chip, firmware), may store one or more sets of instructions that areexecutable by a processor of the computer 42 to perform the steps ofmethod 58. In accordance with present embodiments, the processor, inperforming method 58, may generate one or more images corrected via MMC.

Turning to FIG. 2, in the depicted implementation, the method 58includes determining detection coefficients 60 for each pixel of thedetector 28 (block 62). The detection coefficients 60 are only obtainedonce for each pixel and may be used for subsequent scans. The detectioncoefficients 60 are a function of the incident photon energy of eachindividual pixel. The detection coefficients 60 are captured from thedata of 4 kVp air scans during spectral calibration. The detectioncoefficients enable the modeling of the detector signals. The detectioncoefficient 60 of pixel i is expressed in polynomial form in thefollowing equation:ε(E,i)=Σ₀ ^(N-1) X _(n)(i)E ^(n),  (1)where ε(E, i) represents the detection coefficient, E represents thephoton energy, i represents the pixel index, X_(n)(i) representsdetection coefficients expressed in polynomial form, and N representsthe number of kVp air scans during the spectral calibration. N is basedon the number of kVp stations. For example, N may range from 4 to 5. Thedetection efficiency factor may depend on a number of factors such asdifferent kVps and different filtrations. In certain embodiments, theX_(n)(i) values may be stored, e.g., in memory 46, for use in MMC.

The detection coefficients 60 are utilized in computing a materiallinearization function (e.g., mapping function) 65 or beam hardeningprojection error for each pixel (block 64) using projections synthesizedthrough system modeling as described in greater detail below. Themapping function 65 for each pixel is designed to linearize materialprojections for the respective pixel. In general, MMC is designed tore-map the detected signals so that the signals are all linearlyproportional to each of the material's length with proper slope. Theslope is a fixed value for each individual material that does not changefrom view to view. The slope assigned to each material can be any valuein principle. But in practice, it should be very close to theattenuation coefficient at the effective energy (i.e., keV) of the beam.This keeps the correction small enough that the original noise ismaintained and, thus, is more forgivable to errors in the materialsegmentation and characterization. As mentioned above, the mappingfunction for MMC is based on individual pixels. This individualpixel-based approach removes general physics beam hardening andvariation in detector spectral response or absorption. As described ingreater detail below, the mapping function 65 is generated based on twobasis materials (e.g., water and iodine) in one embodiment. Other basismaterial pairs may be chosen from other materials such as calcium,metal, and bone. The use of two basis materials enables a complex bodycomposition to be simplified into two components. This reduces the needfor forward projections for other materials (i.e., those not selected asthe basis materials), while also reducing the complexity of the mappingfunction.

After determining the mapping function for each pixel, the method 58includes obtaining projection data 66 (e.g., datasets) (block 68), forexample, by acquiring the projection data 66 via the CT system 10described above. The method 58 also includes reconstructing theprojection data 66 from the plurality of pixels into a reconstructedimage 67 (e.g., full field of view (FOV) reconstructed image) (block69). The method 58 includes performing material characterization on animage volume (e.g., voxel) of the reconstructed image (block 70) toreduce a number of materials analyzed in each pixel to two basismaterials (e.g., iodine and water). In the absence of k-edge materialsin an object to be imaged, the object can be analyzed as a combinationof two basis materials (e.g., iodine and water) from the physics pointof view. In general, there are four distinct materials in a human body:soft tissue, bone, iodine, and metal implants. Also, if calcium is denseenough, it can approximately be considered as cortical bone. Using thistheory, bone and metal are represented by water and iodine, and thehuman body may be described by a two-material system. As a result beamhardening is completely determined by the combination of two materialprojections. The material characterization enables the transformation ofmultiple materials (e.g., metal, bone, etc.) in the image volume intoproper representations of two basis materials (e.g., water and iodine).As described in greater detail below, the material characterization mayinclude performing material segmentation and inverse basis materialdecomposition.

The method 58 further includes generating a remapped image volume 72(e.g., material-based projection from a re-mapped pixel) (block 74) forat least one basis material (e.g., iodine) of the two basis materials(e.g., iodine and water). In certain embodiments, remapped projections72 may be obtained for both basis materials (e.g., iodine and water). Toutilize MMC, projections involving two basis materials are needed. Forexample, the projections involving the two basis materials include atotal projection (e.g., water and iodine) attenuated by the object,which also represents both basis materials, and a projection contributedby one of the two basis materials (e.g., iodine) that represents thesums of the equivalent portions of each of the materials (e.g.,non-water materials) that is not included in the other basis material ofthe basis material pair. The method 58 yet further includes performingforward projection on the re-mapped image volume 72 (block 76) togenerate a forward projection 78 for at least one basis material (e.g.,iodine) to produce a material-based (e.g., iodine-based) projection.Typically, a forward projection is not necessary for the totalprojection since the total projection from the measurement (i.e.,projection data 66) already exists. Thus, only a single forwardprojection is required. In certain embodiments, forward projections maybe performed on both a re-mapped total projection and the re-mappedprojection of the projection contributed by one of the two basismaterials (e.g., iodine). The image volume is forward-projected usingthe exact system geometry, and the forward projections are interpolatedinto the same ray directions and the same number of views as themeasured projections (e.g., projection data 66) by the detection system,which results in paired data projection sets.

The method 58 includes generating MMC corrected projections 84 (e.g.,linearized projections) for each pixel based on the material-basedprojection 78 and initial total projection (e.g., projection data 66)representing attenuation through both of the two basis materials (e.g.,iodine and water). In particular, the MMC corrected projections 84 maybe based on a summation of the initial total projection and the materiallinearization function 65 or beam hardening projection error (block 86).In certain embodiments, the initial total projection and thelinearization function 65 or beam hardening projection error may besubtracted from each other. The linearization function 65 is based onthe values for the material-based projection 78 and the total initialtotal projection. In certain embodiments, the initial total projectionmay be a spectrally corrected total raw projection. The method 58further includes reconstructing a final MMC reconstructed image 88 fromthe MMC corrected projections 84 (block 90).

FIGS. 3 and 4 illustrate a detailed process flow diagram of anembodiment of a method 92 for performing MMC on projection data thatutilizes iodine and water as the two basis materials. As noted above,other materials may be used for the basis material pair. Any suitableapplication-specific or general-purpose computer having a memory andprocessor may perform some or all of the steps of the method 92. By wayof example, as noted above with respect to FIG. 1, the computer 42 andassociated memory 46 may be configured to perform the method 92. Forexample, the memory 46, which may be any tangible, non-transitory,machine-readable medium (e.g., an optical disc, solid state device,chip, firmware), may store one or more sets of instructions that areexecutable by a processor of the computer 42 to perform the steps ofmethod 92. In accordance with present embodiments, the processor, inperforming method 92, may generate one or more images corrected via MMC.

It should be noted, the method 92 may include determining detectioncoefficients for each pixel of the detector 28 as described in method58. Turning to FIG. 3, in the depicted implementation, the method 58includes obtaining the material linearization function (e.g., mappingfunction) or beam hardening projection error for each pixel based ondetection coefficients and synthesized water and iodine projectionsduring calibration. The mapping function takes a polynomial form for thewater (or water and iodine) and iodine projections. The water and iodineprojections to compute the mapping function are synthesized throughsystem modeling, while the water and iodine projections used in the MMCcorrection described below are obtained from total measured projectionand forward projecting the volume of reconstructed images. The modelingprocess is both accurate and simplistic due to the absence of complexphysical phantoms. In order to obtain the mapping functions, the method92 includes computing raw projections through L_(w), which representsthe thickness of water, and L_(io), which represents the thickness ofiodine. In particular, the method 92 includes computing a total rawprojection (p_(t)) 98 of each pixel attenuated by both water and iodine(block 100) in the following equation:

$\begin{matrix}{{p_{t} = {- {\log\left( \frac{\sum\limits_{E}^{kV}\;{{S_{kv}(E)} \cdot E \cdot {\mathbb{e}}^{{{- {\mu_{w}{(E)}}}L_{w}} - {{\mu_{io}{(E)}}L_{io}}} \cdot {\eta(E)} \cdot {ɛ(E)}}}{\sum\limits_{E}^{kV}\;{{{S_{kv}(E)} \cdot E \cdot \eta}{(E) \cdot {ɛ(E)}}}} \right)}}},} & (2)\end{matrix}$where index kv represents the tube voltage at a given detector rowlocation, E represents the photon energy, S_(kv)(E) represents theincident spectrum, η(E) represents the scintillator stopping power,μ_(w)(E) represents the water mass attenuation coefficient, μ_(io)(E)represents the iodine mass attenuation coefficient, and ε(E) representsthe detection coefficient. The method 92 also includes computing theeffective raw projection (p_(io)) 102 of each pixel contributed byiodine (i.e., attenuated by water) in the following equation:

$\begin{matrix}{p_{io} = {- {{\log\left( \frac{\sum\limits_{E}^{kV}\;{{S_{kv}(E)} \cdot E \cdot {\mathbb{e}}^{{{- {\mu_{w}{(E)}}}L_{w}} - {{\mu_{io}{(E)}}L_{io}}} \cdot {\eta(E)} \cdot {ɛ(E)}}}{\sum\limits_{E}^{kV}\;{{S_{kv}(E)} \cdot E \cdot {\mathbb{e}}^{{- {\mu_{w}{(E)}}}L_{w}} \cdot {\eta(E)} \cdot {ɛ(E)}}} \right)}.}}} & (3)\end{matrix}$The method 92 also includes computing an effective raw projection(p_(w)) 106 of each pixel contributed by water (i.e., attenuated byiodine) in the following equation:

$\begin{matrix}{p_{w} = {- {{\log\left( \frac{\sum\limits_{E}^{kV}\;{{S_{kv}(E)} \cdot E \cdot {\mathbb{e}}^{{- {\mu_{w}{(E)}}}L_{w}} \cdot {\eta(E)} \cdot {ɛ(E)}}}{\sum\limits_{E}^{kV}\;{{{S_{kv}(E)} \cdot E \cdot \eta}{(E) \cdot {ɛ(E)}}}} \right)}.}}} & (4)\end{matrix}$

Upon obtaining the projections, the method 92 includes spectrallycorrecting the raw projections 98, 100 for water beam hardening (block110) to generate a spectrally corrected total projection (P_(t))attenuated by both water and iodine and a spectrally corrected effectiveiodine projection (P_(io)) 112. In particular, the spectrally correctedtotal projection (P_(t)) 112 is obtained by the following:

$\begin{matrix}{{P_{t} = {\sum\limits_{n = 1}^{NR}\;{a_{n}p_{t}^{n}}}},} & (5)\end{matrix}$where NR represents the beam hardening (BH) order and a_(n) representsthe BH coefficients. The BH order may range from 3 to 5. The spectrallycorrected effective iodine projection (P_(io)) 112 is obtained by thefollowing:

$\begin{matrix}{P_{io} = {{\sum\limits_{n = 1}^{NR}\;{a_{n}p_{t}^{n}}} - {\sum\limits_{n = 1}^{NR}\;{a_{n}{p_{w}^{n}.}}}}} & (6)\end{matrix}$

Due to the beam hardening from iodine, linearity does not hold anymoreafter spectral correction. That isP _(t)≠μ₁ L _(w)+μ₂ L _(io)  (7)for all the possible combination of (L_(w), L_(io)), where μ₁ and μ₂ aretwo constants that typically represent the attenuation coefficients atthe effective beam energy. In other words, the polychromatic signal(P_(t)) does not equal the sum of the monochromatic signals μ₁L_(w) andμ₂L_(io). This non-linearity arising from physics is the root cause ofbeam hardening in CT images. The mapping functions correct for suchnon-linearity. The method 92 includes computing the BH error 114 due toiodine (block 116), which is the difference between the sum of themonochromatic signals and the polychromatic signal, as represented by:Δp(P _(t) ,P _(io))=(μ₁ L _(w)+μ₂ L _(io))−P _(t),  (8)where Δp(P_(t),P_(io)) represents the BH error 114.

The method 92 includes generating MMC coefficients (m_(αβ)) 118 for eachpixel (block 120). The MMC coefficients 118 are obtained through fittingthe data pairs {(P_(t),P_(io)) Δp(P_(t),P_(io))} generated in equation8. In other words, the generation of MMC coefficients is based on the BHerror 114, the spectrally corrected total raw projection (P_(t)) 112,and the spectrally corrected iodine projection (P_(io)) 112. The fittingis applied to each individual detector pixel. Thus, the MMC coefficients118 already include a self adjustment to correct for BIS artifacts. Thiseliminates the need for a separate BIS correction step because when MMCis performed, BIS correction is applied automatically.

From simulation, and using the above equations, the method 92 includescapturing the BH error due to iodine as a function of spectrallycorrected raw projections (block 122). In particular, the process ofcapturing the BH error is iterated for L_(w)=0 to 50 cm, step=1 cm, andL_(io)=0 to 3 cm, step=0.15 cm, to enable building a functional table124 of BH error due to iodine against projection values, P_(t) andP_(io). The BH error is expressed in the following polynomial form:

$\begin{matrix}{{\Delta\;{p\left( {P_{t},P_{io}} \right)}} = {\sum\limits_{{\alpha = 0},{\beta = 1}}^{{\alpha = n_{1}},{\beta = n_{2}}}\;{m_{\alpha\;\beta}P_{t}^{\alpha}{P_{io}^{\beta}.}}}} & (9)\end{matrix}$In equation (9), P_(t) and P_(io) are to the n₁ and n₂ order,respectively, and these are not constant. A rank up to the third orderis sufficient for both n₁ and n₂. From these equations, the mappingfunctions are obtained that correct for the non-linearity.

After obtaining the material linearization mapping functions, the method92 includes performing material characterization of an image volume 125for of a reconstructed image obtained from reconstructing acquiredprojection data. In particular, the method 92 includes performingmaterial segmentation (block 126) on the image volume 125. Amongdistinct materials in the human body (e.g., soft tissue, bone, iodine,and metal implants), two different algorithms may be utilized for thematerial segmentation. The first algorithm may be Hounsfield units (HU)value (e.g., CT value) based, where the different materials areseparated based off on designated HU levels and/or ranges representativeof each material. The second algorithm may be used for bone tracking, inparticular, to separate soft bone from iodine. The method 92 may utilizethe first algorithm or both the first and second algorithm for materialsegmentation. In certain embodiments, the composition of the human bodymay be segmented into more detailed components such as fat, muscle,stent, calcification, and so forth, which can be integrated into themethod 92. In addition, other information may be used to guidesegmentation. For example, if the scan is obtained prior to introductionof a contrast agent, input may be provided to the algorithm that iodineis not present in the image. Additionally, pre-contrast agent scans maybe used as prior information for post-contrast scan correction. Inparticular, pre-contrast agent images may provide detailed informationon the location and size of the bone region and used to further guidesegmentation.

Upon performing material segmentation, the method 92 includes performinginverse basis material decomposition (block 128) on the differentsegmented projection data. In particular, the inverse basis materialdecomposition transforms or converts the materials other than iodine andwater (i.e., bone and metal) to the basis materials iodine and water.From a physics point of view, neither bone nor metal projections areindependent from iodine and metal (and thus the BH error need not be afunction of bone and metal projections). Instead, the bone and metalprojections are a linear combination of water and iodine from thephysics point of view. Thus, the CT values or linear attenuationcoefficients can be expressed as the following:μ_(linear)(bone)=(m _(bw)μ_(eff) _(—) _(mass)(water)+m _(bio)μ_(eff)_(—) _(mass)(iodine))·D _(b)  (10)andμ_(linear)(metal)=(m _(mw)μ_(eff) _(—) _(mass)(water)+m _(mio)μ_(eff)_(—) _(mass)(iodine))·D _(m),  (11)where μ_(linear)(bone) and μ_(linear)(metal) represent the effectivelinear attenuation coefficients of bone and metal, respectively. Also,μ_(eff) _(—) _(mass)(water) and μ_(eff) _(—) _(mass)(iodine) representthe effective mass attenuation coefficients of water and iodine under agiven incident spectrum, respectively. Coefficients m_(bw), m_(bio),m_(mw), and m_(mio) are the material decomposition coefficients of boneand metal onto water and iodine basis, and these coefficients areconstants, which only depend on the type of bone and metal. For example,the type of bone and metal may be cortical bone and titanium,respectively. In certain embodiments, if a stent is segmented, itsdecomposition can also be applied. D_(b) and D_(m) are the densityvalues of bone and metal, typically expressed in g/cc, which areconverted from the HU values by stripping off their correspondingeffective mass attenuation coefficients. As a result of equations (10)and (11), the spectral responses of bone and metal are decomposed intothose of water and iodine, which simplifies a complex object bynarrowing the BH effects to those of two basis materials, water andiodine.

Alternative to equations (10) and (11), the material decomposition todetermine the equivalent iodine fraction from other materials other thaniodine may be performed by using the effective keV or using the densityof a material to be decomposed. In the effective keV approach, for avoxel identified as material X (let its CT number be HU_(x)) whichcontains material T and pure material X, the following may berepresented as:HU _(x)=(1−σ)HU _(T) +σHU _(PX).  (12)HU_(T) represents the CT number for material T, HU_(PX) represents theCT number for the pure material X, and

$\begin{matrix}{\sigma = {\frac{{HU}_{x} - {HU}_{T}}{{HU}_{PX} - {HU}_{T}}.}} & (13)\end{matrix}$Then, the iodine fraction (expressed by HU) can be computed as

$\begin{matrix}{{{HU}_{xio} \approx {m_{xio} \times R \times {HU}_{PX} \times \frac{{HU}_{x} - {HU}_{T}}{{HU}_{PX} - {HU}_{T}}}},{when}} & (14) \\{{R = \frac{\left( \frac{\mu}{\rho} \right)_{io}\left( \overset{\_}{E} \right)}{\left( \frac{\mu}{\rho} \right)_{PX}\left( \overset{\_}{E} \right)}},} & (15)\end{matrix}$where R is a ratio dependent on the selected effective keV (Ē) andm_(xio) is the material decomposition factor of material X for iodine,assuming

$\begin{matrix}{{\left( \frac{\mu}{\rho} \right)_{PX}(E)} = {{{m_{xw}\left( \frac{\mu}{\rho} \right)}_{w}(E)} + {{m_{xio}\left( \frac{\mu}{\rho} \right)}_{io}{(E).}}}} & (16)\end{matrix}$When material T is air, HU_(T)=0; when material T is water, HU_(T)=1000.In the approach that uses the density of the material to be decomposed,the iodine fraction can be computed as

$\begin{matrix}{{{HU}_{xio} \approx {\left( {{HU}_{PX} - {1000\; m_{xw}\rho_{PX}}} \right) \times \frac{{HU}_{x} - {HU}_{T}}{{HU}_{PX} - {HU}_{T}}}},} & (17)\end{matrix}$where ρ_(PX) is the density for pure material X.

To perform MMC, projections of two materials are need, the totalprojection (i.e., water and iodine) and the iodine projection (i.e.,iodine equivalent portion of the non-water materials). The method 92includes generating a re-mapped image volume 130 (block 132) for theiodine equivalent portion of each of the non-water materials summedtogether. The re-mapping process is described in the following equation:V(x,y,z)=D _(iodine)(x,y,z)+m _(bio) D _(b)(x,y,z)+m _(mio) D_(m)(x,y,z),  (18)where x, y, z represent the Cartesian coordinate of a pixel in theimage, V(x,y,z) represents the re-mapped projection for the iodineequivalent portion of each of the non-water materials summed together,and D_(iodine)(x,y,z) represents the value of the segmented pixelidentified as iodine solution with water density subtracted.

The method 92 also includes generating a forward projection 134 of theiodine equivalent portion based on the re-mapped projection 130generated in equation (18) (block 136). The total projection (i.e.,water and iodine) can be obtained from the measurement (i.e., spectrallycorrected projection 112 (P_(t))). In certain embodiments, the totalprojection may be obtained through a forward projection as well.However, only using a single forward projection (i.e., for iodineforward projection 134) speeds up the processing. The remapped imagevolume 130 is forward-projected using the exact system geometry, and theforward projections are interpolated into the same ray directions, andthe same number of views as the measured projections by the detectionsystem, resulting in paired data projections sets.

After obtaining the paired data projections sets, the method 92 includesdetermining the BH projection error (Δp) 138 (block 140). As describedabove, a functional BH error table 124 is generated. The BH projectionerror 138 (i.e., material linearization function) for each pixel may beobtained from the BH error table 124 via the total projection value(i.e., spectrally corrected total projection 112) and the iodineequivalent forward projection 134 value. The method 92 also includesgenerating MMC corrected projections 142 for each pixel based on thetotal projection value (i.e., spectrally corrected total projection 112)and the BH projection error (block 144) as described in the followingequation:P _(corr) =P _(t) +Δp.  (19)P_(corr) represents the final signal for each pixel to be reconstructed.The correction can be performed in the projection domain or the imagedomain if the initial image volume and the final volume are bothreconstructed with full field of view (FOV). However, in clinical cases,ROI reconstruction is often needed. To obtain the un-truncated forwardprojection, the initial volume has to be in full FOV, but can be in areduced matrix. For a reduced matrix, a decimation of 2 in all x-y-zdirections is suggested. In other words, it may be preferred that theMMC correction term is added to the original projections to form a newset of corrected projections. The method 92 further includesreconstructing the final MMC corrected image 146 (block 148) from theMMC corrected projections 142.

The initial image volume for each pixel (i.e., projection data 94) mayalready include HU value contamination from BH and scatter in theinitial volume due to the mean value of non-water material not beingaccurate. This may lead to some inaccuracy in the iodine equivalentprojections extracted from forward projecting the re-mapped volume. Thismay lead to some level of inaccuracy in MMC of a second order. Upondetermining if there is sufficient processing time (block 150), the MMCmay be reiterated by returning to the material segmentation (block 136)and repeating the remaining process steps, such that more precise iodineprojections are obtained from the image volume corrected by thefirst-pass MMC. If there is no remaining processing time, thenreiteration of the process is not performed.

Throughout the above description of methods 58, 92, all the parametersand coefficients are built on physics, as opposed to empirically basedtechniques, and there are no tuning parameters. In principle, thereshould be no need for any adjustment to the correction. However, linearscaling factors may be used at various points in the methods 58, 92 toaccount for any inaccuracies in the modeling. For example, possibletuning places may include scaling forward projected iodine projectionsto adjust for inaccuracy due to BH in the initial image and scaling theBH error values to adjust for inaccuracy in the beam spectrum modeling.

In another embodiment, each pixel may be characterized or segmented intothree basis materials (e.g., water, iodine, and bone). The techniquesdescribed above may be used based on the volume fractions of the threebasis materials. Thus, for the theoretical calculation of water andiodine, a bone projection may be generated in a similar manner. Whenusing three basis materials, two forward projections may be needed asopposed to a single projection. However, using three basis materials mayimprove the robustness of the multi-material correction algorithm.

Technical effects of the disclosed embodiments include providing a MMCapproach to minimize artifacts in reconstructed images due to beamhardening, heel-effect related spectral variation, and BIS that utilizesa single second-pass correction. In addition, the MMC approachlinearizes the detection of all the materials to eliminate beamhardening from its root cause, regardless of the material type. Thisresults in more accurate and consistent CT values of bone, soft tissue,and contrast agent for better clinical diagnosis. Direct clinicalbenefits of the MMC approach include improved image quality, betterdifferentiation between cysts and metastases, and accurate contrastmeasurement in CT perfusion.

This written description uses examples to disclose the subject matter,including the best mode, and also to enable any person skilled in theart to practice the subject matter, including making and using anydevices or systems and performing any incorporated methods. Thepatentable scope of the subject matter is defined by the claims, and mayinclude other examples that occur to those skilled in the art. Suchother examples are intended to be within the scope of the claims if theyhave structural elements that do not differ from the literal language ofthe claims, or if they include equivalent structural elements withinsubstantial differences from the literal languages of the claims.

The invention claimed is:
 1. A method comprising: acquiring projectiondata of an object from a plurality of pixels; reconstructing theacquired projection data from the plurality of pixels into areconstructed image; performing material characterization anddecomposition of an image volume of the reconstructed image to reduce anumber of materials analyzed in the image volume to two basis materials;generating a re-mapped image volume for at least one basis material ofthe two basis materials; performing forward projection on at least there-mapped image volume for the at least one basis material to produce amaterial-based projection; and generating multi-material correctedprojections based on the material-based projection and a totalprojection attenuated by the object, which represents both of the twobasis materials, wherein the multi-material corrected projectionscomprise linearized projections.
 2. The method of claim 1, comprisingcomputing a material linearization function for each pixel of theplurality of pixels, wherein the respective material linearizationfunction for each pixel is used to generate the linearized projections.3. The method of claim 2, wherein computing the material linearizationfunction for each pixel comprises computing for each pixel a total rawprojection attenuated by both of the two basis materials and aneffective raw projection contributed by the at least one basis material.4. The method of claim 3, comprising computing for each pixel spectrallycorrected raw projections for water beam hardening for both the totalraw projection and the effective raw projection contributed by the atleast one basis material.
 5. The method of claim 3, wherein the totalprojection attenuated by both of the two basis materials comprises thespectrally corrected total raw projection.
 6. The method of claim 3,comprising computing for each pixel a beam hardening error due to the atleast one basis material based at least on the spectrally correctedtotal raw projection.
 7. The method of claim 6, comprising generatingfor each pixel multi-material correction (MMC) coefficients based atleast on the beam hardening error, the spectrally corrected total rawprojection, and the spectrally corrected effective raw projectioncontributed by the at least one basis material for the respective pixel.8. The method of claim 7, wherein the MMC coefficients are self-adjustedto correct for bone-induced spectral artifacts during the generation ofthe multi-material corrected projections for each pixel.
 9. The methodof claim 7, comprising determining a detection coefficient for eachpixel of a detector for utilization in computing the materiallinearization function for each pixel.
 10. The method of claim 9,comprising generating a table of beam hardening errors for each pixel asa function of the MMC coefficients, the spectrally corrected total rawprojection, and the spectrally corrected effective raw projectioncontributed by the at least one basis material for the respective pixelusing an analytical physics model and the detection coefficients. 11.The method of claim 1, wherein performing material characterization ofthe image volume comprises performing material segmentation of the imagevolume.
 12. The method of claim 1, wherein performing materialcharacterization of the image volume comprises performing inverse basismaterial decomposition on the image volume to convert materials otherthan the two basis materials to the two basis materials.
 13. The methodof claim 1, comprising reconstructing a final multi-material correctedimage from the multi-material corrected projections.
 14. One or morenon-transitory computer-readable media encoding one or moreprocessor-executable routines, wherein the one or more routines, whenexecuted by a processor, cause acts to be performed comprising:acquiring projection data of an object from a plurality of pixels;reconstructing the acquired projection data from the plurality of pixelsinto a reconstructed image; performing material characterization of animage volume of the reconstructed image to reduce a number of materialsanalyzed to two basis materials; generating a re-mapped image volume forat least one basis material of the two basis materials; performingforward projection on at least the re-mapped image volume for the atleast one basis material to produce a material-based projection; andgenerating multi-material corrected projections based on thematerial-based projection and a spectrally corrected total rawprojection attenuated by the object, which represents both of the twobasis materials, wherein the multi-material corrected projectionscomprise linearized projections.
 15. The one or more non-transitorycomputer-readable media of claim 14, wherein the one or more-routines,when executed by the processor, cause further acts to be performedcomprising: computing a material linearization function for each pixelof the plurality of pixels, wherein the respective materiallinearization function for each pixel is used to generate the linearizedprojections.
 16. The one or more non-transitory computer-readable mediaof claim 15, wherein the one or more routines, when executed by theprocessor, cause further acts to be performed comprising: computing foreach pixel a total raw projection attenuated by both of the two basismaterials and an effective raw projection contributed by the at leastone basis material when computing the material linearization functionfor each pixel.
 17. The one or more non-transitory computer-readablemedia of claim 16, wherein the one or more routines, when executed bythe processor, cause further acts to be performed comprising: computingfor each pixel spectrally corrected raw projections for water beamhardening for both the total raw projection and the effective rawprojection contributed by the at least one basis material.
 18. The oneor more non-transitory computer-readable media of claim 16, wherein theone or more routines, when executed by the processor, cause further actsto be performed comprising: computing for each pixel a beam hardeningerror due to the at least one basis material based at least on thespectrally corrected total raw projection.
 19. The one or morenon-transitory computer-readable media of claim 18, wherein the one ormore routines, when executed by the processor, cause further acts to beperformed comprising: generating for each pixel multi-materialcorrection (MMC) coefficients based at least on the beam hardeningerror, the spectrally corrected effective raw projection contributed bythe at least one basis material for the respective pixel.
 20. The one ormore non-transitory computer-readable media of claim 19, wherein the oneor more routines, when executed by the processor, cause further acts tobe performed comprising: generating a table of beam hardening errors foreach pixel as a function of the MMC coefficients, the spectrallycorrected total raw projection, and the spectrally corrected effectiveraw projection contributed by the at least one basis material for therespective pixel, wherein the MMC coefficients are self-adjusted tocorrect for bone-induced spectral artifacts during the generation of themulti-material corrected projections for each pixel.
 21. The one or morenon-transitory computer-readable media of claim 15, wherein the one ormore routines, when executed by the processor, cause further acts to beperformed comprising: performing inverse basis material decomposition onthe image volume to convert materials other than the two basis materialsto the two basis materials when performing material characterization ofthe image volume.
 22. The one or more non-transitory computer-readablemedia of claim 15, wherein the one or more routines, when executed bythe processor, cause further acts to be performed comprising:reconstructing a final multi-material corrected image from themulti-material corrected projections.
 23. A system comprising: a memorystructure encoding one or more processor-executable routines wherein theroutines, when executed cause acts to be performed comprising: acquiringprojection data of an object from a plurality of pixels; reconstructingthe acquired projection data from the plurality of pixels into areconstructed image; performing material characterization of an imagevolume of the reconstructed image to reduce a number of materialsanalyzed to two basis materials; generating a re-mapped image volume forat least one basis material of the two basis materials; performingforward projection on at least the re-mapped image volume for the atleast one basis material to produce an material-based projection; andgenerating multi-material corrected projections based on thematerial-based projection and a spectrally corrected total rawprojection attenuated by the object, which also represents both of thetwo basis materials, wherein the multi-material corrected projectionscomprise linearized projections; and a processing component configuredto access and execute the one or more routines encoded by the memorystructure.
 24. The system of claim 23, wherein the routines, whenexecuted by the processor, cause further acts to be performedcomprising: performing inverse basis material decomposition on the imagevolume to convert the materials other than the two basis materials tothe two basis materials when performing material characterization of theimage volume.
 25. The system of claim 23, wherein the routines, whenexecuted by the processor, cause further acts to be performedcomprising: computing for each pixel a beam hardening error due to theat least one basis material based at least on the spectrally correctedtotal raw projection; and generating for each pixel multi-materialcorrection (MMC) coefficients based at least on the beam hardeningerror, the spectrally corrected total raw projection, and a spectrallycorrected raw projection contributed by the at least one basis materialfor the respective pixel, wherein the MMC coefficients are self-adjustedto correct for bone-induced spectral artifacts during the generation ofthe multi-material corrected projections for each pixel.
 26. A methodcomprising: acquiring projection data of an object from a plurality ofpixels; reconstructing the acquired projection data from the pluralityof pixels into a reconstructed image; performing materialcharacterization and decomposition of an image volume of thereconstructed image to reduce a number of materials analyzed in theimage volume to two basis materials; generating a re-mapped image volumefor at least one basis material of the two basis materials; performingforward projection on at least the re-mapped image volume for the atleast one basis material to produce a material-based projection; andgenerating multi-material corrected projections based on thematerial-based projection and a total projection attenuated by theobject, which represents both of the two basis materials.